2008 iTest Problems/Problem 34
Problem
While entertaining his younger sister Alexis, Michael drew two different cards from an ordinary deck of playing cards. Let a be the probability that the cards are of different ranks. Compute 
.
Solutions
Solution 1
Use complementary counting to count the number of ways one can draw two cards with the same rank. There are 
ranks, and each rank has 
cards. That means the probability of getting two cards with the same rank is 
, so the probability of getting two cards with different ranks is 
. That means 
.
Solution 2
The first card can be any card, so the probability is 
. However, of the 
cards remaining, only 
of them have a different rank. Thus, the probability of getting two cards with different ranks is 
, so .
See Also
| 2008 iTest (Problems) | ||
| Preceded by: Problem 33 |
Followed by: Problem 35 | |
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